Device specific finite element models for simulating endovascular treatment

ABSTRACT

Systems and methods provide a novel computational approach to planning the endovascular treatment of cardiovascular diseases. In particular, the invention simulates medical device deployment and hemodynamic outcomes using a virtual patient-specific anatomical model of the area to be treated, high-fidelity finite element medical device models and computational fluid dynamics (CFD). In an embodiment, the described approach investigates the effects of coil packing density, coil shape, aneurysmal neck size and parent vessel flow rate on aneurysmal hemodynamics. A processor may receive patient clinical data used to construct the relevant anatomical structure model. The processor may access medical device models constructed using finite element analysis and three dimensional beam analysis, and simulates the deployment of selected medical devices in the anatomical structure model. The selected medical device models and the anatomical structure model mesh, allowing the processor to simulate hemodynamic outcomes using computational fluid dynamics.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 14/605,887, filed Jan. 26, 2015, entitled “DEVICESPECIFIC FINITE ELEMENT MODELS FOR SIMULATING ENDOVASCULAR TREATMENT,”which claims the benefit of U.S. Provisional Application No. 61/996,972,filed May 22, 2014, entitled “DEVICE SPECIFIC FINITE ELEMENT MODELS FORSIMULATING ENDOVASCULAR TREATMENT,” and U.S. Provisional Application No.61/996,971, filed Jan. 27, 2014, entitled “DEVICE SPECIFIC FINITEELEMENT MODELS FOR SIMULATING ENDOVASCULAR TREATMENT.” All of theseapplications are incorporated by reference in their entireties.Furthermore, any and all priority claims identified in the ApplicationData Sheet, or any correction thereto, are hereby incorporated byreference under 37 C.F.R. § 1.57.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under Grant No. 1151232awarded by the National Science Foundation. The U.S. government hascertain rights in the invention.

BACKGROUND Field

The present invention is generally related to medical device deploymentsimulations. The present invention more particularly relates to a systemand method for simulating the endovascular deployment of a medicaldevice and the hemodynamic outcomes of its placement.

Description of the Related Art

A cerebral aneurysm is a cerebral vascular disorder in which weakness ofthe wall of a cerebral artery or vein causes a localized dilation orballooning of the blood vessel wall. Cerebral aneurysms are classifiedby both size and shape. Smaller aneurysms produce few, if any, symptoms.Larger aneurysms may cause severe headaches, nausea, vision impairment,vomiting and/or loss of consciousness. Larger aneurysms have greatertendency to rupture, but, the majority of ruptured aneurysms are small.About 50 percent of patients die immediately after rupture. In addition,ruptured cerebral aneurysms account for about 10 percent of all strokes.

For those 50 percent who survive, there are currently two conventionaltreatment options to stop the bleeding from a cerebral aneurysm as wellas reduce the potential for recurrence: (1) surgical clipping; and (2)endovascular treatment. One or the other of these procedures must beperformed within 24 hours of the rupture for optimal results. Surgicalclipping involves removing the aneurysm at its base using a clip that isthereafter left to close the vessel wall. This procedure is currentlydone open, in the form of a craniotomy (i.e., cutting into the skull toaccess the brain), which carries with it significant risks.

Endovascular treatment involves the insertion of a medical device insidethe aneurysm balloon or inside the affected blood vessel to preventrebleeding. This procedure is performed intraluminally (i.e., fromwithin the blood vessel and not requiring a cut into the skull) via thefemoral or carotid artery and a microcatheter. Oftentimes, a stent,which is basically an expandable hollow bridge, is used to assist indeploying the coil into the aneurysm sac. The treatment works bypromoting blood clotting around the coils, eventually sealing theaneurysm and reducing pressure on its outer wall.

Other endovascular treatments are being developed, including but notlimited to flow diverter stents. Flow diverter stent devices block theopening at the base of the aneurysm (where it meets the vessel wall),preventing blood from flowing into the aneurysm sac.

It should be noted that endovascular treatments may be performed onpatients who are diagnosed with cerebral aneurysms prior to rupture.Recent advances in medical imaging have increased early diagnosis ofcerebral aneurysms by 75 percent, offering the promise of eradication ofthis silent killer.

Unfortunately, endovascular treatments carry risks. With respect toendovascular coiling, which is the most common type of endovasculartreatment, recurrence rates related to post-procedure hemodynamics areas high as 50 percent relative to certain types of cerebral aneurysms.Also, intra-operative mortality occurs in 5-10 percent of theendovascular cerebral aneurysm treatment cases. As such, there is a needto improve these outcomes.

The medical simulation community has developed clinical training toolsthat simulate endovascular medical device placement. (See Cotin, et al.,U.S. Application Publication No. U.S. 2008/0020362 A1.) These tools,however, construct a simplistic medical device model, ignore or simplifyfluid dynamic simulations, do not construct an anatomical model from thepatient's image data, and use a haptic device, which ultimately presentsan unrealistic and unreliable post-treatment fluid dynamic prediction.(See also, simulation platforms produced by medical simulation companiesknown as Mentice, Simsuite and Simbionix). Others have invented a systemand method for virtually designing a medical device conformed for usewith a specific patient. (See Anderson, et al, U.S. Pat. No. 7,371,067B2.) Such invention focused on virtually modeling a specific anatomicsite and simulating the interaction between the anatomical model and avirtual medical device designed specifically for that patient.

The systems and methods disclosed herein seek to improve endovascularmedical device placement procedure outcomes by taking into account thepatient's clinical data and both the fluid dynamics of thepost-procedure blood flow conditions and the structural dynamics ofcommercially available medical devices via simulation in order to ensurethe most appropriate device(s) is/are ultimately used.

SUMMARY

The devices of the present invention have several features, no singleone of which is solely responsible for its desirable attributes. Withoutlimiting the scope of this invention as expressed by the claims whichfollow, its more prominent features will now be discussed briefly. Afterconsidering this discussion, and particularly after reading the sectionentitled “Detailed Description,” one will understand how the features ofthis invention provide several advantages over current designs.

An aspect of the present disclosure provides a system for simulatingmedical device dynamics. The system includes a database configured tostore medical device models and one or more processors. The one or moreprocessors are configured to virtually construct an anatomical structuremodel of a patient, simulate a deployment of a plurality of the medicaldevice models in the anatomical structure model, and simulatehemodynamic outcomes of the deployment of the plurality of the medicaldevice models in the anatomical structure model.

Another aspect of the present disclosure provides a method forsimulating medical device dynamics. The method includes storing acomputer readable database comprising medical device models,constructing, by the one or more processors, an anatomical structuremodel based on patient clinical data, simulating a deployment of aplurality of the medical device models in the anatomical structuremodel, and simulating hemodynamic outcomes of the deployment of theplurality of the medical device models in the anatomical structuremodel.

Another aspect of the present disclosure provides a method forsimulating medical device dynamics. The method includes receiving, byone or more processors, an anatomical structure model for a patient, theanatomical structure model comprising one or more blood vessels and atleast one flow rate within one or more of the blood vessels, receiving aselection of one or more medical device models from a collection ofmedical device models stored in a database, simulating, by the one ormore processors, a deployment of the selected medical device models inthe anatomical structure model, and simulating hemodynamic outcomes ofthe deployment.

Another aspect of the present disclosure provides a method of simulatingnavigation of a virtual medical device through a vessel. The methodincludes modeling, by one or more computers, advancing a crimped medicaldevice disposed in a catheter along a centerline of a simulated bloodvessel to a site of an aneurysm, and modeling, by the one or morecomputers, unsheathing the crimped medical device from the catheter atthe site of the aneurysm.

Another aspect of the present disclosure provides a method of simulatingnavigation of a virtual medical device through a vessel. The methodincludes defining boundary conditions for navigation of a virtualmedical device through a simulated blood vessel, defining loads to applyto the virtual medical device during the navigation, and applying thedefined loads, in view of the defined boundary conditions, to thevirtual medical device during navigation along a centerline of thesimulated blood vessel to a site of an aneurysm.

An aspect of the present disclosure provides for a novel computationalapproach to planning the endovascular treatment of cardiovasculardiseases. In particular, the invention simulates medical devicedeployment and hemodynamic outcomes using a virtual patient-specificanatomical model of the area to be treated, high-fidelity finite elementmedical device models and computational fluid dynamics (CFD). In anembodiment, the described approach investigates the effects of coilpacking density, coil shape, aneurysmal neck size and parent vessel flowrate on aneurysmal hemodynamics.

Another aspect of the present disclosure provides a cloud-based highperformance data processing system for simulating medical devicedynamics. The data processing system includes a computer cluster havinga user interface configured to receive patient clinical data. Thepatient clinical data may be used to virtually construct the relevantanatomical structure model. A server coupled to the computer cluster mayhave a database configured to store a plurality of medical devicemodels. The medical device models may be constructed using finiteelement analysis and three dimensional beam analysis, and the userselects one or more medical device models from the database. Thecomputer cluster may be further configured to simulate the deployment ofthe selected medical device(s) into the anatomical structure model, andthe selected medical device model(s) and the anatomical structure modelmesh. The computer cluster may be further configured to simulatehemodynamic outcomes using computational fluid dynamics.

Yet another aspect of the present disclosure provides a computerizedmethod for simulating medical device dynamics that receives, by acomputer cluster, patient clinical data. That patient clinical data maybe used to virtually construct the relevant anatomical structure model.The method also stores a computer readable database configured tocomprise a plurality of medical device models. The medical device modelsmay be constructed using finite element analysis and three dimensionalbeam analysis. The user selects one or more medical device models fromthe database, and the computer cluster then simulates the deployment ofthe selected medical device(s) in the anatomical structure model, andthe selected medical device model(s) and the anatomical structure modelmesh. Finally, the method simulates hemodynamic outcomes usingcomputational fluid dynamics.

In one implementation, the present disclosure provides a system forsimulating medical device dynamics. The system may include a computercluster having a user interface configured to receive clinical data of apatient, and a server coupled to the computer cluster. The clinical datamay be used to virtually construct an anatomical structure model of thepatient. The server may have a database configured to store a pluralityof medical device models constructed using finite element analysis andthree dimensional beam analysis, and the user may use the user interfaceto select one or more of the medical device models from the database.The computer cluster may be configured to simulate a deployment of eachof the selected medical device models in the anatomical structure modelsuch that the selected medical device models and the anatomicalstructure model mesh. The computer cluster may be further configured touse the meshing of the selected medical device models and the anatomicalstructure model to simulate hemodynamic outcomes of the deployment ofthe selected medical devices in the anatomical structure model usingcomputational fluid dynamics.

The anatomical structure model may include one or more blood vessels,and may further include at least one flow rate within one or more of theblood vessels. The computer cluster may be configured to construct theplurality of medical device models. One or more of the medical devicemodels may be an embolic coil, and each of the one or more embolic coilsmay be a complex coil or a helical coil. One or more of the medicaldevice models may be a stent, and each of the one or more stents may bean enterprise stent, a Neuroform stent, or a flow diverter. Theanatomical structure model may include a computational model, and eachof the medical device models comprise one or both of a surface mesh anda CAD geometry. Simulating the deployment of each of the selectedmedical device models in the anatomical structure model may includegenerating one or more surface meshes and one or more blood volumemeshes from the meshing of the selected medical device models and theanatomical structure model. The computer cluster may be configured toautomatically simulate the deployment of a plurality of medical devicesin the anatomical model.

In another implementation, the present disclosure provides a method forsimulating medical device dynamics, the method steps being performed bya computer cluster. The method may include receiving patient clinicaldata used to construct an anatomical structure model, storing a computerreadable database containing a plurality of medical device models eachconstructed using finite element analysis and three dimensional beamanalysis, receiving a selection of one or more of the medical devicemodels from the database, simulating a deployment of the selectedmedical device models in the anatomical structure model, and simulatinghemodynamic outcomes of the deployment using computational fluiddynamics using one or more meshes of the selected medical device modelsand the anatomical structure model. Simulating the deployment mayinclude creating the one or more meshes of the selected medical devicemodels and the anatomical structure model. Each of the selected medicaldevice models may be either an embolic coil or flow diverter comprisinga plurality of beam elements or a high porosity stent comprising arepeating geometry of cells. The one or more meshes may include one orboth of a surface mesh and a volume mesh.

When the selected medical device model is an embolic coil, creating theone or more meshes may include sweeping each of the beam elements usinga circular surface of a first diameter to produce swept embolic coilsurfaces, applying a mesh density function to the anatomical structuremodel and the coil surface mesh, defining one or more body partsrepresenting blood volume and solid volume, and discretizing the bodyparts into the meshes. When the selected medical device model is a highporosity stent, creating the one or more meshes may include constructinga virtual topology of the stent surface, defining a maximum mesh elementsize and a minimum mesh element size for the cells applying a pluralityof volume-mesh filling points to exclude overlapping regions from thegeometry, generating a volume mesh encompassing the stent and comprisingone or more layers including an outermost layer, generating a surfacemesh by projecting the outermost layer of the volume mesh onto the stentsurface, converting the surface mesh into a facet geometry, applying amesh density function to a blood volume within the anatomical structuremodel near the facet geometry, defining one or more body partsrepresenting blood volume and solid volume, and discretizing the bodyparts into the meshes.

In another implementation, the present disclosure provides anothermethod for simulating medical device dynamics, the method steps beingperformed by a computer cluster. The method may include receiving ananatomical structure model for a patient including one or more bloodvessels and at least one flow rate within one or more of the bloodvessels receiving a selection of one or more medical device models froma collection of medical device models stored in a database, simulating adeployment of the selected medical device models in the anatomicalstructure model, and simulating hemodynamic outcomes of the deployment.Simulating the deployment may include connecting the selected medicaldevice model to a microcatheter model and advancing the microcathetermodel into the anatomical structure model. Simulating the deployment mayinclude modeling contacts between the selected medical device model andthe anatomical structure model with a penalty contact enforcementalgorithm. The method may further include creating one or more of themedical device models in the collection of medical device models.

Further aspects, features and advantages of the present invention willbecome apparent from the detailed description that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentinvention will now be described in connection with embodiments of thepresent invention, in reference to the accompanying drawings. Theillustrated embodiments, however, are merely examples and are notintended to limit the invention. Some embodiments will be described inconjunction with the appended drawings, where like designations denotelike elements.

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying drawings in which correspondingreference symbols indicate corresponding parts.

FIG. 1 is a flowchart of a treatment planning method in accordance withthe present disclosure.

FIGS. 2A-C are diagrams of exemplary structures for endovascular coils.

FIG. 3A-B are graphs demonstrating serial linkage of beam elements usingthree-dimensional beam theory.

FIG. 4 is a graph of an external force-based approach to modeling coilmemory shape.

FIG. 5 is a graph of an exemplary computational geometry of a complex(spherical) shaped coil for modeling coil memory shape.

FIGS. 6A-D are diagrams of exemplary finite element coil deploymentvalidations against physical coil deployments.

FIGS. 7A-B are diagrams of exemplary high-porosity stent designs.

FIG. 8 is a multiple-step diagram of the construction of a stent havingthe design of FIG. 7B.

FIG. 9 is a flowchart of a method of modeling a virtual stentdeployment.

FIG. 10 is a diagram of a virtual catheter navigation based on thevessel centerline.

FIG. 11 is a diagram of an application of radial boundary constraintsand constraint relaxation for a virtual stent during deployment.

FIG. 12A is a diagram of a surface mesh of a single endovascular coil.

FIG. 12B is a diagram of a cross-section of a volume mesh representingblood volume in a coiled basilar-tip aneurysm.

The various features illustrated in the drawings may not be drawn toscale. Accordingly, the dimensions of the various features may bearbitrarily expanded or reduced for clarity. In addition, some of thedrawings may not depict all of the components of a given system, methodor device. Finally, like reference numerals may be used to denote likefeatures throughout the specification and figures.

DETAILED DESCRIPTION

In the following description, and for the purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of the various aspects of the invention. It will beunderstood, however, by those skilled in the relevant arts, that thepresent invention may be practiced without these specific details. Inother instances, known structures and devices are shown or discussedmore generally in order to avoid obscuring the invention. In many cases,a description of the operation is sufficient to enable one to implementthe various forms of the invention, particularly when the operation isto be implemented in software. It should be noted that there are manydifferent and alternative configurations, devices and technologies towhich the disclosed inventions may be applied. The full scope of theinventions is not limited to the examples that are described below.

FIG. 1 depicts an overview of the present treatment planning system. Thesystem can be performed by a computer, computer cluster, processor, orserver as described herein. The system implements a method of planning amedical treatment for a patient in which: at step 100, a user of thesystem enters patient data at a workstation 102; at step 110, thepatient data is uploaded to a system server, where it is used toconstruct a model of the relevant anatomical structure; at step 120, theuser selects the medical devices 122 he/she wishes to have deployed in avirtual model of the patient; at step 130, device deployment issimulated according to a design treatment; and, at step 140, the virtualpatient's hemodynamic outcome is simulated as described below. Themethod may be employed by one or more software modules executed by aprocessor. In certain embodiments, the system steps are repeated withthe user varying the medical devices selected. However, the system mayalso automatically simulate different medical devices and/or differentsizes of a medical device. For example, several different sizes ofcomplex coils may be successfully deployed into an aneurysm sac, butwith varying results; the system may receive an indication (e.g., from aphysician) that a particular complex coil is the desired treatment, andmay automatically simulate deployment, according to the methods below,of a plurality of sizes of the selected complex coil and may provide(e.g., within the report of step 150) a recommendation for theappropriate size of coil. In some embodiments, the system may select thedifferent devices or different device sizes without input from the user.Once all desired simulations are complete, at step 150 the system mayprovide a report comparing the hemodynamic outcomes and medical deviceperformance of each alternative treatment combination.

Simulating Endovascular Device Deployment

In the past, finite element (FE) analysis was used to aid in the designand optimization of medical devices during manufacture. Its use tosimulate device dynamics during deployment has been significantlylimited, however, due to several technical challenges. These challengesinclude, but are not limited to, complex geometries, non-lineardeformations and numerous contact interactions. This invention proposesnovel FE approaches for overcoming the technical barriers associatedwith simulating endovascular device deployment. The developed FEapproaches consider the structural properties, design specifications anddeployment mechanics of endovascular devices.

Modeling Embolic Coils

As shown in FIG. 2A, embolic coils may be constructed from a thin metalwire 200, with diameter (D₁), which is wound into a secondary helicalstructure 202 with diameter (D₂). The helical structure 202 is thenshaped into a tertiary structural configuration 204 having a specificcoil loop diameter (D₃). Coils may have many different tertiarystructures or “shapes.” The two most common coil shapes are helical(FIG. 2B) and complex (FIG. 2C). Referring to FIG. 2C, complex coils 206are spherical, “yarn-like” structures in which each coil loop 208 isaligned at a different angle. Coil shape and size (determined bydiameter D₃) influence aneurysmal filling and coil distribution in thesac, while the thickness of the metal wire (diameter D₁) and thediameter D₂ of the helical wind determine coil stiffness.

FE Coil Model

In a FE coil model, embolic coils may be modeled using three dimensional(3D) beam theory. Referring to FIGS. 3A-B, each coil may be representedby a set of serially linked 3D beam elements 300, where each beam iscomposed of two or three nodes 302 a, 302 b that connect to adjacentelements 300. The element 300 may have up to six degrees of freedom ateach node 302 a, 302 b, as shown by axial rotations θ_(jy), θ_(jx), andθ_(jz) around orthogonal vectors v_(jy), v_(jx), and v_(jz),respectively. Ninety-two percent platinum and eight percent tungstenmaterial compositions were specified for the coils, which resulted in aYoung's modulus of 7.5 GPa and a density of 21.3 g/cm3. A Poisson ratioof 0.39 was also prescribed, following the assumption that the stockmetal wire of the coil was tightly wound and can be approximated as ahollow beam element with a thickness equivalent to the coil filamentdiameter and primarily made of platinum. The coils may be virtuallyplaced in a 0.4 mm diameter rigid catheter or microcatheter anddigitally discretized with a mesh resolution of 1.5×D₂. Finer meshresolutions may be used, but may result in considerable overclosurebetween adjacent coil loops.

Any suitable approach may be used to model coil memory shape. In oneembodiment, the coil memory shape may be modeled using an externalforce-based approach; alternatively or additionally, for example, anelastic strain energy-based approach may be used. In the externalforce-based approach, concentrated load forces may be exerted onto thebeam element nodes to specify coil shape and loop size. The concentratednodal loads may be applied, at a constant magnitude, throughout thesimulation to force the coil into a specific configuration. In theelastic strain energy-based approach, the coil shape may be modeled byapplying initial stresses and strains onto the beam element nodes. Theinitial stresses and strains impart internal elastic forces onto thebeam elements until the coil reaches its lowest strain energy point.

More particularly, in the force-based approach, parametric equations maybe applied through a subroutine to specify coil shape and loop size.Referring to FIG. 4, the interconnected beam elements 300 may be modeledwithin a catheter, sheath enclosure, or microcatheter 400, andconcentrated load forces 402 may be exerted on the beam element 300nodes (e.g., 302 a) in each Cartesian direction X, Y, Z (it will beunderstood that the arrows representing the load forces 400 may bepointing in any 3D direction) according to the parametric equations. Theparametric equations were derived by estimating the force F_(mag)required to displace a beam element by D₃/2 using the equation:

F _(mag)=[K _(e)]U

where [K_(e)] is the stiffness matrix of the beam element and U is thevector of displacements. F_(mag) may then be multiplied by the forcedistribution or shape of the coil (i.e., the scaling and direction ofthe force). Two different force distributions have been investigated: acomplex or spherical distribution and a helical distribution, eachillustrated further below. The complex distribution was modeled as a 3Dcurve with multiple helical loops rotated around a sphere at differentangles, which is similar to the described geometry of physical complexcoils. The helical distribution was modeled as helical loopsperpendicular to the main axis of the straight set of beam elements,which is similar to the geometry of helical coils.

An embodiment of a complex shape force distribution is illustrated inFIG. 5 and referred to herein by its parametric equation C_(shape).C_(shape) may be constructed by taking a point P describing a circle ona sphere and rotating it along the x (R_(x)), y (R_(y)), then z (R_(z))axis at different rotation angles (γ,β, and α).

P=(cos(θ),sin(θ),0)

f ₁ =R _(x)(P,γ)

f ₂ =R _(y)(f ₁,β)

C _(shape) =R _(z)(f ₂,α)

Different rotation angles were selected for each axis and rotationangles were varied linearly along the main axis of the wire (positionsZ_(i)).

θ=Z _(i)*λ

γ=Z _(i)*λ/π

β=*Z _(i)*λ/π²

α=Z _(i)*λ/π³

The above equation for C_(shape) results in a parametric function thatis given by:

C _(shape)=[C _(shape) −x,C _(shape) −y,C _(shape) −z];

which expands into:

C _(shape)−x=cos(γ)*(sin(β*)*(sin(γ)*sin(θ))+cos(β)*cos(θ))−sin(α)*(cos(γ)*sin(θ))

C _(shape)−y=sin(α)*(sin(β)*(sin(γ)*sin(θ))+cos(β)*cos(θ))+cos(α)*(cos(γ)*sin(θ))

C _(shape) −z=cos(β)*(sin(γ)*sin(θ))−sin(β)*cos(θ).

In the illustrated embodiment, loop diameter D₃ may be prescribed using:

λ=1.7601*D ₃ ^(−1.028)

which presents the relationship between λ and the loop diameter D₃. Therelationship is determined by first calculating the mean circumferenceof all the loops in C_(shape) for a given value of λ. D₃ may then becalculated from the mean circumference and plotted against λ. Anexponential curve according to the equation above for λ may thus be usedto fit the data.

A helical force distribution may be modeled after helical coils, whichwhen deployed can form helical loops perpendicular to the catheter,sheath enclosure, or microcatheter 400 axis. Accordingly, a parametricequation, H_(shape), may represent the geometry of a helix perpendicularto the main axis of the straight wire. Coil loop diameter (D₃) may bespecified by defining the number of turns N in the helix. N is given by:

N=L/(πD ₃)

where L is the length of the wire divided by the circumference of eachloop (assuming negligible vertical separation between loops). Theequation of a helix in the Y and Z axes can be represented by

Y=cos(2πN)

Z=sin(2πN)

Substituting the equation for N leads to the parametric equation forH_(shape):

H _(shapeY)=cos(2/(D ₃ *Z _(i)))

H _(shapeZ)=sin(2/(D ₃ *Z _(i))).

Note that H_(shape) is defined only for the Y and Z axis. Where no forceis applied in the X axis, the vertical distance between the loops may bedetermined by the helical wind diameter (D₂).

In the strain-based approach, initial stresses and strains are appliedto beam elements 300 placed in the catheter 400. The imposed strains andstresses impart elastic energy onto the structure which is given by:

E=Σ∫v _(e)σ^(T) ∈dV

where σ and ϵ are defined below. During simulation, the internal elasticforces drive the coil back to its original configuration.

The initial stresses and strains may be defined by first creating thegeometry of the deployed coil in air. Coil geometries may be constructedby multiplying loop diameter and coil shape (i.e., D₃C_(shape) andD₃H_(shape)). Material orientations may be defined to align the straincomponents with the coil geometry's local orientation. The coil may thenstretched into a straight wire. The generated stresses and strains maythen be applied to the series of beam elements 300 in the microcatheter400.

Solving Equations of Motion

The dynamic equation of motion of a structure can be written as:

[M]ü+[C]{dot over (u)}+[K]u=F _(ext)

where [M], [C] and [K] are the mass, dampening and stiffness matrices ofthe structure. F_(ext) is the vector of external load and u, {dot over(u)} and ü are the displacement, velocity, and acceleration vectors. Theequation can be solved using direct integration numerical schemes. Thereare many different integration schemes that can be used. Due to thecomplex contact interactions involved in simulating device deployment,an embodiment of an explicit integration scheme may be used. The schemeperforms well in highly non-linear, dynamic problems that involvemultiple contact interactions. Further, it represents a straight forwardapproach to solving complex non-linear systems, wherein a solution ismarched forward in time without solving a system of coupled equations ateach time increment. The solution for this embodiment is calculated byfirst determining accelerations within the system, using the governingequation:

ü ^((t)) =M ⁻¹(F _(ext) ^((i)) −I _(int) ^((i)))

where ü^((i)) is the acceleration at current time i, M is the massmatrix, and F_(ext) and I_(int) are the vectors of external and internalnodal forces, respectively. The computation of this equation isinexpensive as M is a diagonal matrix consisting of lumped masses at thenodes of each beam element.

Next, ü^((i)) is used to calculate the velocity u and displacement u atlater time increments.

$u^{{({i + \frac{1}{2}})} =} = {u^{i - \frac{1}{2}} + {\frac{{\Delta \; t^{({i + 1})}} + {\Delta \; t^{(i)}}}{2}u^{(i)}}}$$u^{({i + 1})} = {u^{(i)} + {\Delta \; t^{({i + 1})}u^{({i + \frac{1}{2}})}}}$

The explicit scheme is non-iterative and is therefore associated withlow computational cost per time increment. However, the explicit schemeis conditionally stable, requiring a very small time-step to stabilizethe solution. The stability limit of the explicit scheme is determinedby the highest eigenvalue in the system ω_(max).

Δt _(c)≤(2/ω_(max))

The limit can also be expressed as the time it takes for information totravel between adjacent nodes using the equation:

Δtc=min(L ^(e) /c ^(d))

where L^(e) is the characteristic element length and c^(d) is thedilational wave speed, which is governed by the elastodynamic equationsof motion:

$c^{d} = \sqrt{\frac{\lambda + {2\mu}}{\rho}}$

where λ and μ are elastic constants and ρ is the material density.

The vector of displacements u at increment i+1 is then used to calculatethe elemental strains ϵ using the equation:

$\epsilon = {\int\frac{u_{{node}\; 1} - u_{{node}\; 2}}{L_{e}}}$

Stresses in the system σ are calculated as a function of strain:

σ(t+Δt)=f(σt,AΔ∈)

For a linear elastic material, the relationship between stress andstrain is governed by the equation:

σ=[D]∈

where [D] is the elasticity matrix. This equation can also be written inmatrix form as:

$\begin{bmatrix}\sigma_{x} \\\sigma_{y} \\\sigma_{z} \\\tau_{xy} \\\tau_{yz} \\\tau_{xz}\end{bmatrix} = {\begin{bmatrix}{{2\mu} + \lambda} & \lambda & \lambda & 0 & 0 & 0 \\\lambda & {{2\mu} + \lambda} & \lambda & 0 & 0 & 0 \\\lambda & \lambda & {{2\mu} + \lambda} & 0 & 0 & 0 \\0 & 0 & 0 & \mu & 0 & 0 \\0 & 0 & 0 & 0 & \mu & 0 \\0 & 0 & 0 & 0 & 0 & \mu\end{bmatrix}\begin{bmatrix}ɛ_{x} \\ɛ_{y} \\ɛ_{z} \\\gamma_{xy} \\\gamma_{yz} \\\gamma_{xz}\end{bmatrix}}$

The internal nodal forces I_(e) at t+Δt may then be assembled using thevalue of σ at t:

I _(e)=∫_(Ve)[B]^(T)σ_(t+Δt) dV

where [B] is the strain displacement matrix, which contains the secondderivative of the shape function of each element.

$\lbrack B\rbrack = {{\frac{d^{2}}{{dx}^{2}}N} = \left\lbrack {{N_{1}^{*}(x)}{N_{2}^{*}(x)}{N_{3}^{*}(x)}{N_{4}^{*}(x)}} \right\rbrack}$

In the case of beam elements, the shape function is given by:

$N_{1} = \left\lbrack {1 - {3\left( \frac{x^{2}}{L} \right)} + {2\left( \frac{x}{L} \right)^{3}}} \right\rbrack$$N_{2} = \left\lbrack {1 - \left( \frac{x}{L} \right)} \right\rbrack^{2}$$N_{3} = {{3\left( \frac{x}{L} \right)^{2}} - {2\left( \frac{x}{L} \right)^{3}}}$$N_{4} = {x\left\lbrack {\left( \frac{x}{L} \right)^{2} - \left( \frac{x}{L} \right)} \right\rbrack}$

where x represents nodal coordinates.

Modeling Contacts

A penalty contact enforcement algorithm may be used to model contactinteractions during device deployment. The algorithm is better suitedfor contacts involving rigid bodies and node elements, and provides lessstringent constraints than kinematic contact models. It is based on amaster/slave formulation, where the slave surface is subordinate to themaster surface. Contact is detected when the slave surface nodespenetrate the master surface's facets. Penetration is resolved bycalculating the spring “stiffness” or resisting force required to opposepenetration. The force is calculated using the depth of the slave node'spenetration, its mass, and the time increment. Combinations of penaltyand kinematic contacts may also be used to model contact interactionsduring device deployment.

A finite sliding formulation may be used to define the type of contactallowed. The formulation allows arbitrary separation, sliding, androtation of the surfaces during contact. However, the formulationassumes that the tangential motion between surfaces does not exceed thefacet size of the master surface within one time increment. Thisassumption complies with the explicit scheme used because of its smalltime increments. The finite-sliding formulation also assumes that themaster surface has continuous surface normals at all points. If themaster surface normals are discontinuous, then slave nodes may becomeconfined in certain regions. Therefore, the master surface is smoothedto remove any sharp transitions in geometry.

A contact tracking algorithm may be used to track the minimum distancebetween the master surface and each slave node at each increment duringsimulation. The tracking algorithm may be divided into a global and alocal contact search component. The global search is the mostcomputationally expensive component of the tracking algorithm and isresponsible for finding the nearest master surface facet for each slavenode. To reduce computational cost, a bucket sorting algorithm may beused. The computational cost may be further reduced by implementing theglobal search once every 100 increments. A local search may be performedin subsequent increments until the next global search. The local searchonly tracks master surface facets that were previously tracked in thelast increment.

When the master and slave surfaces are in contact, a friction model maybe used to determine whether the slave node slips or sticks. Thefrictional model follows Coulomb's friction law, which states that thetangential motion is limited by the product of the frictionalcoefficient μ and the normal traction t_(N).

|t _(t) |<μ|t _(N)|

Nodes that fulfill this equation stick to the surface, while nodes thatdo not fulfill the equation slide along the surface with

|t _(t) |<μ|t _(N)|.

In an embodiment of virtually deploying the coils, a displacementboundary condition may be prescribed at the distal node to guide thecoil into the sac, which simulates the clinical coil pusher used invivo. A penalty contact enforcement algorithm may be used to model self,coil-to-coil, coil-to-catheter, and coil-to-aneurysm interactions.Coil-to-catheter interactions were assumed to be frictionless to accountfor catheter lubrication. Frictional coefficients of 0.4 and 0.2 wereprescribed for the coil-to-aneurysm and coil-to-coil interactions,respectively.

Finite element coil deployments were rigorously validated against invitro and in vivo deployments. One such validation is shown in FIG. 6,where simulated finite element deployments (boxes (a) and (c)) arecompared against in vitro helical and complex coil deployments (boxes(b) and (d)) in identical aneurysm models.

Modeling Stents and Flow Diverters

While the present invention may be used to effectively model anysuitable porous stent, two embodiments of high porosity stents aredescribed herein by way of example: (1) a Neuroform stent; and (2) anEnterprise stent. Both stents are composed of Nitinol, a Nickel-Titaniumalloy, and have an estimated porosity of 90%. However, the stents differin design, as shown in FIGS. 7A-B. The Neuroform stent 700 features anopen cell design and consists of eight sinusoidal crown segments. Theopen cell design of the Neuroform stent 700 enhances its flexibility intortuous vessels and provides it with a high radial force, whichtranslates to better vessel conformability at acute angle bends. EachNeuroform stent 700 strut 702 has an estimated thickness of about 70 μm.

The Enterprise stent 710 features a closed cell 712 design with flaredends 714, 716. Advantages of the closed cell design include smaller pore718 sizes, which translate to better coverage of the aneurysm neck, andreduced risk of stent protrusion into the aneurysm during deployment,which is a common unfavorable deployment outcome for open cell designs.However, stents with closed cell designs typically have a lower radialforce (among stents with the same strut thickness) and poorerconformability to the vessel wall at acute angle bends. Each Enterprisestent 710 strut 720 has an estimated thickness of about 90 μm.

Flow diverters are stent-like devices that are deployed across theaneurysmal orifice in order to divert blood away from the aneurysmalsac. They are commonly self-expandable devices with low stent porosityand feature braided tubular structures. One example of a flow diverteris the pipeline embolization device (PED), which is composed of 48braided cobalt-chromium alloy strands. Each strand is approximately 30microns in diameter. The stent porosity of the PED varies from 65-70%depending on device configuration and the diameter size of the artery.

Modeling Stent and Flow Diverter Geometry

In an modeling example according to the illustrations, both theNeuroform and Enterprise high porosity stents were constructed inPyformex (pyformex.berlios.de) using a custom built python code. It willbe understood that other programming languages may be equally suitablefor the stent modeling. Referring to FIG. 8, construction of stentgeometries involves: (i) creating a planar base model 800 of a repeatingcell geometry using triangular elements 802, (ii) reflecting andreplicating the geometry to create a 2D version 810 of the stent, and(iii) applying a cylindrical transformation to “roll” a 2D geometry 820into a cylinder 830.

In the case of the Enterprise stent, illustrated in FIG. 8, a Gompertzfunction was first used to construct the base geometry. The function isgiven by

y(x)=αe ^(b) ^(e) ^(cx)

where x is the position and a, b, and c are coefficient values that weredetermined using high resolution images of the Enterprise device. Theresulting triangular meshes were written as stereolithography (STL)files and imported to Geomagic Studio to rectify any intersecting oroverlapping triangular elements. The STL files were then converted toCAD geometries and imported into Abaqus, a finite element solver.

In the case of the PED, 3D beam theory was used, in a manner similar tothat described above for modeling coil geometry, to model individualstrands of the PED. Specifically, each PED strand was represented by aset of serially linked elastic solid 3D beam elements, as illustrated inFIG. 3A-B, with 30 micron diameter. The strands were braided using acustom built mathematical description of the braiding scheme, whichspecifies the pitch (angle between separate strands), number ofclockwise and anti-clockwise strands, diameter and length of the PED,and the diameter of the strands. Cobalt-Chromium alloy materialproperties were imposed onto the beam elements.

The stent and flow diverter geometries were meshed in Abaqus usingtriangular and quadrilateral shell elements. Approximately 6,000-8,000reduced-order triangular shell elements were generated for each stentgeometry. An artificial shell thickness of 70 μm was applied to all theshell elements and hyperelastic material properties were imposed. Thehyperelastic material properties approximate Nitinol's austenite andmartensite material phases at body temperature.

Modeling Stent and Flow Diverter Deployment

FIG. 9 depicts an example three-step simulated deployment of a virtualstent or flow diverter, performed by a computer, computer cluster, orserver as described herein. Generally, this process involves: at step90, “sheathing,” or crimping the geometry 900 of the stent or flowdiverter into the shape of a catheter, sheath enclosure, ormicrocatheter 902; at step 92, advancing the catheter 902 through asimulated blood vessel 904 to the site of the aneurysm 906; and, at step94, unsheathing the geometry 900 by relaxing the radial constraintsapplied at step 90 on all or a portion of the geometry 900 in astep-by-step process. In an embodiment, crimping (step 90) may beperformed by imposing a radial displacement boundary condition (i.e., a“crimper”) onto a cylindrical shell. In one application, the crimper maycompress the geometry 900 into a 0.54 mm catheter 902. The magnitude ofthe radial displacement is applied in time using a smooth step functionto reduce chatter vibration between the geometry 900 and crimper.

After crimping, the catheter 902 is advanced along the vessel 904centerline to the site of the aneurysm 906, which site is shown ingreater detail in FIG. 10. In one application, catheter 902 advancementmay be performed through kinematic coupling between a reference point910 (see FIG. 9), which models a guidewire, and nodes at the catheter902 tip. Displacements and direction normals are calculated using thevessel centerline and then prescribed onto the reference point 910. Inanother embodiment the reference point 910 may also be coupled to thenodes at the tip of the stent or flow diverter.

Referring to FIG. 11, after catheter 902 advancement, the geometry 900may be divided into multiple subsets n₁₋₆, and radial constraints may beapplied to each subset to constrain the stent/flow diverter radius tothe catheter radius, as given by:

r _(stent) −n _(i) −r _(catheter).

To unsheathe the geometry 900 (step 94), step-by-step the radialconstraints on each geometry subset n₁₋₆ may be relaxed, such as inreverse sequence (i.e., beginning at the tip of the geometry 900). Adifferent unsheathing simulation process can be performed by advancing apusher (a component of the stent delivery system) to push the stent/flowdiverter outside the catheter while slowly pulling back the catheter tosimulate stent/flow diverter unsheathing.

Meshing

Meshing of the simulated geometry may be performed to providecomputational data for determining the hemodynamics of the implant. Inthe below-described example implementation of a meshing approach, acomputational model of the untreated cerebral aneurysm, and astereolithography model of the endovascular device geometry wereimported into ANSYS ICEM 12.1 software (ANSYS, Inc., Canonsburg, Pa.,USA) to generate surface and volume meshes.

Meshing Embolic Coils

Beam elements were first swept in Matlab using a custom built code. Thebeam elements were swept using a circular surface with a diameter D₂.The swept embolic coil surfaces were then shrink-wrapped with a maximumtriangular mesh element size of 20 μm to merge different coils andremove any overlapped or intersecting surface elements. The small meshsize ensured that structural details were captured aftershrink-wrapping. Geomagic Studio (Raindrop Geomagic, Durham, N.C.) wasthen used to fill any small holes in the resulting surface mesh. A meshdensity function was applied to the aneurysmal volume and coil surfaces.The density function was employed to adequately resolve the devicegeometry and high flow velocity gradients. Further, the density functionenhanced the mesh quality near the device, resulting in fewer sharptransitions in mesh element size. Multi-body parts were then defined forthe blood and the solid volume. Lastly, the patch independent Octreemesh generator was used to discretize the coil and blood volume into atotal of 19-25 million tetrahedral elements, corresponding to 5-7million nodes. An example of a finalized surface and volume mesh ispresented in FIGS. 12A-B. In particular, FIG. 12A illustrates atetrahedral surface mesh of a single embolic coil 1200, and FIG. 12Billustrates a blood volume mesh 1210 for an example basilar tip aneurysm1220 having the coil 1200 inserted therein. The empty spots 1230 withinthe aneurysm 1220 sac indicate the presence of the coil 1200. The bloodflow volume may be discretized at a higher mesh density (i.e., highernumber of triangular or tetrahedral elements per unit volume) in theregion of the aneurysm 1220 sac to better resolve complicated flowdynamics that occur in those areas, as compared to simpler flows such asapproximate the basilar split 1240.

Meshing High Porosity Stents

The meshing process for high porosity stents may include theconstruction of a virtual topology of the stent surface. Joint surfacesand edges may be merged using a defined set tolerance. Maximum andminimum mesh element sizes may then be defined for the virtual cells.

In the case of telescoping stents, some intersecting or overlappingregions may be present because of the penalty contact formulation used.Overlaps may be excluded from the geometry through the use of avolume-mesh filling approach. In this approach, multiple filling pointsmay be defined for a single telescoped stent body. The Octree meshgenerator may be used as above to create a volume mesh that encompassesall the stent bodies. After volume mesh generation, the Octree solverprojects the outermost volume mesh layer onto the stent surfaceresulting in a single, merged, surface mesh of several telescopingstents. The volume mesh may be discarded, and the surface mesh may beconverted into a facet geometry with non-intersecting edges retained.

A mesh density function may be applied to the blood volume near thefaceted stent. The final blood and stent volume mesh may be generatedusing the same techniques outlined for embolic coils. Lastly, thegenerated surface and volume meshes may be imported into ANSYS Fluentsoftware (ANSYS, Inc., Canonsburg, Pa., USA) for fluid dynamicsimulation.

Meshing Flow Diverters

Each set of beam elements representing a flow diverter strand were firstswept in Matlab using a custom built code. Beam elements were swept witha circular surface with a diameter equivalent to the strand diameter ofthe flow diverter. The resulting swept model was imported into ANSYSICEM and a mesh density function was applied around the flow divertergeometry. Multi-body parts were then defined for the blood and flowdiverter volume. Last, the patch independent Octree method was employedto discretize the blood and flow diverter volume into 30-40 milliontetrahedral elements.

The terms “processor”, as used herein is a broad term, and is to begiven its ordinary and customary meaning to a person of ordinary skillin the art (and is not to be limited to a special or customizedmeaning), and refer without limitation to a computer system, statemachine, processor, or the like designed to perform arithmetic or logicoperations using logic circuitry that responds to and processes thebasic instructions that drive a computer. In some embodiments, the termscan include ROM and/or RAM associated therewith.

As used herein, the term “determining” encompasses a wide variety ofactions. For example, “determining” may include calculating, computing,processing, deriving, investigating, looking up (e.g., looking up in atable, a database or another data structure), ascertaining and the like.Also, “determining” may include receiving (e.g., receiving information),accessing (e.g., accessing data in a memory) and the like. Also,“determining” may include resolving, selecting, choosing, establishingand the like.

The various operations of methods described above may be performed byany suitable means capable of performing the operations, such as varioushardware and/or software component(s), circuits, and/or module(s).Generally, any operations illustrated in the Figures may be performed bycorresponding functional means capable of performing the operations.

The various illustrative logical steps, blocks, modules and circuitsdescribed in connection with the present disclosure (such as the stepsof FIGS. 1 and 9) may be implemented or performed with a general purposeprocessor, a digital signal processor (DSP), an application specificintegrated circuit (ASIC), a field programmable gate array signal (FPGA)or other programmable logic device (PLD), discrete gate or transistorlogic, discrete hardware components or any combination thereof designedto perform the functions described herein. A general purpose processormay be a microprocessor, but in the alternative, the processor may beany commercially available processor, controller, microcontroller orstate machine. A processor may also be implemented as a combination ofcomputing devices, e.g., a combination of a DSP and a microprocessor, aplurality of microprocessors, one or more microprocessors in conjunctionwith a DSP core, or any other such configuration.

In one or more aspects, the functions described may be implemented inhardware, software, firmware, or any combination thereof. If implementedin software, the functions may be stored on or transmitted over as oneor more instructions or code on a computer-readable medium.Computer-readable media includes both computer storage media andcommunication media including any medium that facilitates transfer of acomputer program from one place to another. A storage media may be anyavailable media that can be accessed by a computer. By way of example,and not limitation, such computer-readable media can comprise RAM, ROM,EEPROM, CD-ROM or other optical disk storage, magnetic disk storage orother magnetic storage devices, or any other medium that can be used tocarry or store desired program code in the form of instructions or datastructures and that can be accessed by a computer. Also, any connectionis properly termed a computer-readable medium. For example, if thesoftware is transmitted from a website, server, or other remote sourceusing a coaxial cable, fiber optic cable, twisted pair, digitalsubscriber line (DSL), or wireless technologies such as infrared, radio,and microwave, then the coaxial cable, fiber optic cable, twisted pair,DSL, or wireless technologies such as infrared, radio, and microwave areincluded in the definition of medium. Disk and disc, as used herein,includes compact disc (CD), laser disc, optical disc, digital versatiledisc (DVD), floppy disk and blu-ray disc where disks usually reproducedata magnetically, while discs reproduce data optically with lasers.Thus, in some aspects computer readable medium may comprisenon-transitory computer readable medium (e.g., tangible media). Inaddition, in some aspects computer readable medium may comprisetransitory computer readable medium (e.g., a signal). Combinations ofthe above should also be included within the scope of computer-readablemedia.

The methods disclosed herein comprise one or more steps or actions forachieving the described method. The method steps and/or actions may beinterchanged with one another without departing from the scope of theclaims. In other words, unless a specific order of steps or actions isspecified, the order and/or use of specific steps and/or actions may bemodified without departing from the scope of the claims.

Thus, certain aspects may comprise a computer program product forperforming the operations presented herein. For example, such a computerprogram product may comprise a computer readable medium havinginstructions stored (and/or encoded) thereon, the instructions beingexecutable by one or more processors to perform the operations describedherein. For certain aspects, the computer program product may includepackaging material.

Software or instructions may also be transmitted over a transmissionmedium. For example, if the software is transmitted from a web site,server, or other remote source using a coaxial cable, fiber optic cable,twisted pair, digital subscriber line (DSL), or wireless technologiessuch as infrared, radio, and microwave, then the coaxial cable, fiberoptic cable, twisted pair, DSL, or wireless technologies such asinfrared, radio, and microwave are included in the definition oftransmission medium.

Further, it should be appreciated that modules and/or other appropriatemeans for performing the methods and techniques described herein can bedownloaded and/or otherwise obtained by an electronic communicationdevice as applicable. For example, such a device can be coupled to aserver to facilitate the transfer of means for performing the methodsdescribed herein. Alternatively, various methods described herein can beprovided via storage means (e.g., RAM, ROM, a physical storage mediumsuch as a compact disc (CD) or floppy disk, etc.), such that anelectronic communication device can obtain the various methods uponcoupling or providing the storage means to the device. Moreover, anyother suitable technique for providing the methods and techniquesdescribed herein to a device can be utilized.

It is to be understood that the claims are not limited to the preciseconfiguration and components illustrated above. Various modifications,changes and variations may be made in the arrangement, operation anddetails of the methods and apparatus described above without departingfrom the scope of the claims.

Unless otherwise defined, all terms (including technical and scientificterms) are to be given their ordinary and customary meaning to a personof ordinary skill in the art, and are not to be limited to a special orcustomized meaning unless expressly so defined herein. It should benoted that the use of particular terminology when describing certainfeatures or aspects of the disclosure should not be taken to imply thatthe terminology is being re-defined herein to be restricted to includeany specific characteristics of the features or aspects of thedisclosure with which that terminology is associated. Terms and phrasesused in this application, and variations thereof, especially in theappended claims, unless otherwise expressly stated, should be construedas open ended as opposed to limiting. As examples of the foregoing, theterm ‘including’ should be read to mean ‘including, without limitation,’‘including but not limited to,’ or the like; the term ‘comprising’ asused herein is synonymous with ‘including,’ ‘containing,’ or‘characterized by,’ and is inclusive or open-ended and does not excludeadditional, unrecited elements or method steps; the term ‘having’ shouldbe interpreted as ‘having at least;’ the term ‘includes’ should beinterpreted as ‘includes but is not limited to;’ the term ‘example’ isused to provide exemplary instances of the item in discussion, not anexhaustive or limiting list thereof; adjectives such as ‘known’,‘normal’, ‘standard’, and terms of similar meaning should not beconstrued as limiting the item described to a given time period or to anitem available as of a given time, but instead should be read toencompass known, normal, or standard technologies that may be availableor known now or at any time in the future; and use of terms like‘preferably,’ ‘preferred,’ ‘desired,’ or ‘desirable,’ and words ofsimilar meaning should not be understood as implying that certainfeatures are critical, essential, or even important to the structure orfunction of the invention, but instead as merely intended to highlightalternative or additional features that may or may not be utilized in aparticular embodiment of the invention. Likewise, a group of itemslinked with the conjunction ‘and’ should not be read as requiring thateach and every one of those items be present in the grouping, but rathershould be read as ‘and/or’ unless expressly stated otherwise. Similarly,a group of items linked with the conjunction ‘or’ should not be read asrequiring mutual exclusivity among that group, but rather should be readas ‘and/or’ unless expressly stated otherwise.

Where a range of values is provided, it is understood that the upper andlower limit and each intervening value between the upper and lower limitof the range is encompassed within the embodiments.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations may be expressly set forth herein for sakeof clarity. The indefinite article “a” or “an” does not exclude aplurality. A single processor or other unit may fulfill the functions ofseveral items recited in the claims. The mere fact that certain measuresare recited in mutually different dependent claims does not indicatethat a combination of these measures cannot be used to advantage. Anyreference signs in the claims should not be construed as limiting thescope.

It will be further understood by those within the art that if a specificnumber of an introduced claim recitation is intended, such an intentwill be explicitly recited in the claim, and in the absence of suchrecitation no such intent is present. For example, as an aid tounderstanding, the following appended claims may contain usage of theintroductory phrases “at least one” and “one or more” to introduce claimrecitations. However, the use of such phrases should not be construed toimply that the introduction of a claim recitation by the indefinitearticles “a” or “an” limits any particular claim containing suchintroduced claim recitation to embodiments containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should typically be interpreted to mean “atleast one” or “one or more”); the same holds true for the use ofdefinite articles used to introduce claim recitations. In addition, evenif a specific number of an introduced claim recitation is explicitlyrecited, those skilled in the art will recognize that such recitationshould typically be interpreted to mean at least the recited number(e.g., the bare recitation of “two recitations,” without othermodifiers, typically means at least two recitations, or two or morerecitations). Furthermore, in those instances where a conventionanalogous to “at least one of A, B, and C, etc.” is used, in generalsuch a construction is intended in the sense one having skill in the artwould understand the convention, e.g., as including any combination ofthe listed items, including single members (e.g., “a system having atleast one of A, B, and C” would include but not be limited to systemsthat have A alone, B alone, C alone, A and B together, A and C together,B and C together, and/or A, B, and C together, etc.). In those instanceswhere a convention analogous to “at least one of A, B, or C, etc.” isused, in general such a construction is intended in the sense one havingskill in the art would understand the convention (e.g., “a system havingat least one of A, B, or C” would include but not be limited to systemsthat have A alone, B alone, C alone, A and B together, A and C together,B and C together, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

Headings are included herein for reference and to aid in locatingvarious sections. These headings are not intended to limit the scope ofthe concepts described with respect thereto. Such concepts may haveapplicability throughout the entire specification.

The foregoing illustrated embodiments have been provided solely forillustrating the functional principles of the present invention and arenot intended to be limiting. For example, the present invention may bepracticed using different overall structural configuration andmaterials. Persons skilled in the art will appreciate that modificationsand alterations of the embodiments described herein can be made withoutdeparting from the spirit, principles, or scope of the presentinvention. The present invention is intended to encompass allmodifications, substitutions, alterations, and equivalents within thespirit and scope of the following appended claims.

What is claimed is:
 1. A system for simulating medical device dynamics,the system comprising: a database configured to store medical devicemodels of different sized flow diverters, each model comprising aplurality of braided strands, each strand being represented by aplurality of serially linked beam elements with a virtual diameter thatis equal to a diameter of the strand; a user interface configured toreceive clinical data of a patient, wherein the user interface isconfigured to allow a user to select a plurality of the medical devicemodels from the database; and one or more processors configured to:virtually construct each of the medical device models by modeling theplurality of braided strands to have a pitch and a number of clockwiseand anti-clockwise strands; virtually construct an anatomical structuremodel of the patient; simulate a deployment of the plurality of themedical device models in the anatomical structure model by: modelingcrimping of each medical device model of the plurality of medical devicemodel into a shape of a microcatheter; and modeling advancing of eachcrimped medical device model along a centerline of a vessel of theanatomical structure model by applying displacement boundary conditionsto nodes at a distal tip of the virtual microcatheter to guide thevirtual microcatheter along the centerline of the vessel to a treatmentregion of the anatomical structure model, and generating at least onesurface mesh and at least one blood volume mesh by (1) sweeping the beamelements of each strand of the medical device model with a circularsurface having the diameter of the strand, and (2) applying an Octreemesh filing technique to the at least one blood volume; modelingunsheathing of each crimped medical device model; simulate hemodynamicoutcomes after simulating the deployment of the plurality of the medicaldevice models in the anatomical structure model; generate a reportcomprising one or more of hemodynamic outcome data and medical devicemodel performance data; and select a medical device for use in anendovascular medical device placement procedure based at least in parton one or more of the hemodynamic outcome data and the medical devicemodel performance data.
 2. The system of claim 1, wherein the storedmedical device models are constructed using finite element modeling andthree dimensional beam theory.
 3. The system of claim 1, whereinsimulating hemodynamic outcomes comprises applying computational fluiddynamics.
 4. The system of claim 1, wherein the one or more processorsare arranged in a computer cluster.
 5. The system of claim 1, whereinthe anatomical structure model comprises one or more blood vessels. 6.The system of claim 5, wherein the anatomical structure model comprisesat least one flow rate within one or more of the blood vessels.
 7. Thesystem of claim 1, wherein the anatomical structure model comprises acomputational model.
 8. The system of claim 1, wherein the medicaldevice models comprise one or both of a surface mesh and a CAD geometry.9. The system of claim 1, wherein simulating the deployment comprisesmodeling contacts between each medical device model and the anatomicalstructure model with a penalty contact enforcement algorithm.
 10. Thesystem of claim 1, wherein the flow diverter is self-expandable and hasa braided tubular structure.
 11. The system of claim 1, wherein the flowdiverter is a pipeline embolization device (PED).
 12. The system ofclaim 1, wherein the flow diverter comprises 48 braided cobalt-chromiumalloy strands.
 13. The system of claim 1, wherein each strand isapproximately 30 microns in diameter.
 14. A method for simulatingmedical device dynamics, the method comprising: storing a computerreadable database comprising medical device models of different sizedflow diverters, each model comprising a plurality of braided strands,each strand being represented by a plurality of serially linked beamelements with a virtual diameter that is equal to a diameter of thestrand; receiving clinical data of a patient; selecting a plurality ofthe medical device models from the database; virtually constructing, bythe one or more processors, each of the medical device models bymodeling the plurality of braided strands to have a pitch and a numberof clockwise and anti-clockwise strands; virtually constructing, by theone or more processors, an anatomical structure model based on thepatient clinical data; simulating a deployment of the plurality of themedical device models in the anatomical structure model; simulatinghemodynamic outcomes after simulating the deployment of the plurality ofthe medical device models in the anatomical structure model; generatinga report comprising one or more of hemodynamic outcome data and medicaldevice model performance data; and selecting a medical device for use inan endovascular medical device placement procedure based at least inpart on one or more of the hemodynamic outcome data and the medicaldevice model performance data.
 15. The method of claim 14, wherein thestored medical device models are constructed using finite elementmodeling and three dimensional beam theory.
 16. The method of claim 14,wherein simulating hemodynamic outcomes comprises applying computationalfluid dynamics.
 17. The method of claim 14, wherein the anatomicalstructure model comprises one or more blood vessels.
 18. A system forsimulating medical device dynamics, the system comprising: a databaseconfigured to store medical device models of different sized flowdiverters, each model comprising a plurality of braided strands, eachstrand being represented by a plurality of serially linked beam elementswith a virtual diameter that is equal to a diameter of the strand; auser interface configured to receive clinical data of a patient, whereinthe user interface is configured to allow a user to select a pluralityof the medical device models from the database; and one or moreprocessors configured to: virtually construct each of the medical devicemodels by modeling the braided plurality of strands to have a pitch anda number of clockwise and anti-clockwise strands; virtually construct ananatomical structure model of the patient; simulate a deployment of theplurality of the medical device models in the anatomical structuremodel; simulate hemodynamic outcomes after simulating the deployment ofthe plurality of the medical device models in the anatomical structuremodel; generate a report comprising one or more of hemodynamic outcomedata and medical device model performance data; and select a medicaldevice for use in an endovascular medical device placement procedurebased at least in part on one or more of the hemodynamic outcome dataand the medical device model performance data.
 19. The system of claim18, wherein the one or more processors simulating the deploymentcomprises: modeling crimping of each medical device model of theplurality of medical device model into a shape of a microcatheter; andmodeling unsheathing of each crimped medical device model.
 20. Thesystem of claim 19, wherein the one or more processors are furtherconfigured to: model advancing of each crimped medical device modelalong a centerline of a vessel of the anatomical structure model byapplying displacement boundary conditions to nodes at a distal tip ofthe virtual microcatheter to guide the virtual microcatheter along thecenterline of the vessel to a treatment region of the anatomicalstructure model; and generate at least one surface mesh and at least oneblood volume mesh by (1) sweeping the beam elements of each strand ofthe medical device model with a circular surface having the diameter ofthe strand, and (2) applying an Octree mesh filing technique to the atleast one blood volume.